Answer
$|A|=6$ and $|A^{-1}|==\frac{1}{6}$.
Work Step by Step
Let $A$ be given by $$A=\left[ \begin {array}{cccc} 1&-1\\ 2&4
\end {array} \right]
,$$
then we have $A^{-1}=\frac{1}{6}\left[ \begin {array}{cccc} 4&1\\ -2&1
\end {array} \right]$.
Now, $|A|=6$ and $|A^{-1}|=\frac{1}{6^2}6=\frac{1}{6}$. Hence, we verify that
$$|A^{-1}=\frac{1}{|A|}.$$
